Sky Sports sources claim that Villa have told the north London club that they need to produce at least £30m if they want to sign the 22-year-old, and while the Midlands club have lowered their asking price from £40m, Spurs chairman Daniel Levy is trying to drive the price down even further, according to the Mirror.
Tottenham are keen to get the transfer over the line as quickly as possible, with manager Mauricio Pochettino hoping to sign the player before his squad depart for a pre-season tour of America this weekend.
Villa also want the sale of Grealish to be completed as soon as possible, with the club eager to raise funds to resolve the financial difficulties that it endured at the end of last season.
The Midlands club almost faced the prospect of administration and potential liquidation in June after they were issued with a winding-up order regarding an unpaid tax bill.
Villa managed to reach a settlement with Her Majesty's Revenue and Customs (HMRC) but need to generate £50m in player sales in order to avoid financial ruin.
And manager Steve Bruce confirmed earlier this month that Grealish, who played for Villa in a 4-1 pre-season friendly win over Walsall on Tuesday night, will have to be sold in order to escape the possibility of administration.
Bruce told Sky Sports, "We're up against it, let's be open and honest, we might have to make some decisions that might not be easy, we have to generate some money.
"Inevitably that is going to be player sales. There are going to be people that I do not want to sell - and the obvious one is Jack."
Grealish came through the youth team at Villa Park and has been on their books since 2001 - when the player was six years old. He made his Villa debut in 2014 and has gone on to represent them over 100 times in all competitions.
He was instrumental in their quest to the Championship play-offs last season, scoring three times in 27 league appearances before they were beaten 1-0 in the Play-Off Final by Fulham.
He has also been linked with a move to Liverpool over the summer, but his most likely destination is in north London, with Spurs looking to lessen the burden on Christian Eriksen in the attacking midfield position.